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Stepper Motor

Model stepper motor

Library

Rotational Actuators

Description

The Stepper Motor block represents a stepper motor. It uses the input pulse trains, A and B, to control the mechanical output according to the following equations:

where:

• eA and eB are the back emfs induced in the A and B phase windings, respectively.

• iA and iB are the A and B phase winding currents.

• vA and vB are the A and B phase winding voltages.

• Km is the motor torque constant.

• Nr is the number of teeth on each of the two rotor poles. The Full step size parameter is (π/2)/Nr.

• R is the winding resistance.

• L is the winding inductance.

• Rm is the magnetizing resistance.

• B is the rotational damping.

• J is the inertia.

• ω is the rotor speed.

• Θ is the rotor angle.

If the initial rotor is zero or some multiple of (π/2)/Nr, the rotor is aligned with the phase winding of pulse A. This happens when there is a positive current flowing from the A+ to the A- ports and there is no current flowing from the B+ to the B- ports.

Use the Stepper Motor Driver block to create the pulse trains for the Stepper Motor block.

The Stepper Motor block produces a positive torque acting from the mechanical C to R ports when the phase of pulse A leads the phase of pulse B.

Thermal Ports

The block has three optional thermal ports, one for each of the two windings and one for the rotor. These ports are hidden by default. To expose the thermal ports, right-click the block in your model, and then from the context menu select Simscape block choices > Show thermal port. This action displays the thermal ports on the block icon, and adds the Temperature Dependence and Thermal port tabs to the block dialog box. These tabs are described further on this reference page.

Use the thermal ports to simulate the effects of copper resistance and iron losses that convert electrical power to heat. For more information on using thermal ports in actuator blocks, see Simulating Thermal Effects in Rotational and Translational Actuators.

Basic Assumptions and Limitations

The model is based on the following assumptions:

• This model neglects magnetic saturation effects, detent torque, and any magnetic coupling between phases.

• When you select the Start simulation from steady state check box in the Simscape™ Solver Configuration block, this block will not initialize an Initial rotor angle value between –π and π.

Dialog Box and Parameters

Electrical Torque Tab

Phase winding resistance

Resistance of the A and B phase windings. The default value is 0.55 Ω.

Phase winding inductance

Inductance of the A and B phase windings. The default value is 0.0015 H.

Motor torque constant

Motor torque constant Km. The default value is 0.19 N*m/A.

Magnetizing resistance

The total magnetizing resistance seen from each of the phase windings. The value must be greater than zero. The default value is Inf, which implies that there are no iron losses.

Full step size

Step size when changing the polarity of either the A or B phase current. The default value is 1.8°.

Mechanical Tab

Rotor inertia

Resistance of the rotor to change in motor motion. The default value is 4.5e-05 kg*m2. The value can be zero.

Rotor damping

Energy dissipated by the rotor. The default value is 8e-04 N*m/(rad/s). The value can be zero.

Initial rotor speed

Speed of the rotor at the start of the simulation. The default value is 0 rpm.

Initial rotor angle

Angle of the rotor at the start of the simulation. The default value is 0 rad.

Temperature Dependence Tab

This tab appears only for blocks with exposed thermal ports. For more information, see Thermal Ports.

Resistance temperature coefficients, [alpha_A alpha_B]

A 1 by 2 row vector defining the coefficient α in the equation relating resistance to temperature, as described in Thermal Model for Actuator Blocks. The first element corresponds to winding A, and the second to winding B. The default value is for copper, and is [ 0.00393 0.00393 ] 1/K.

Measurement temperature

The temperature for which motor parameters are defined. The default value is 25 C.

Thermal Port Tab

This tab appears only for blocks with exposed thermal ports. For more information, see Thermal Ports.

Winding thermal masses, [M_A M_B]

A 1 by 2 row vector defining the thermal mass for the A and B windings. The thermal mass is the energy required to raise the temperature by one degree. The default value is [ 100 100 ] J/K.

Winding initial temperatures, [T_A T_B]

A 1 by 2 row vector defining the temperature of the A and B thermal ports at the start of simulation. The default value is [ 25 25 ] C.

Rotor thermal mass

The thermal mass of the rotor, that is, the energy required to raise the temperature of the rotor by one degree. The default value is 50 J/K.

Rotor initial temperature

The temperature of the rotor at the start of simulation. The default value is 25 C.

Percentage of magnetizing resistance associated with the rotor

The percentage of the magnetizing resistance associated with the magnetic path through the rotor. It determines how much of the iron loss heating is attributed to the rotor thermal port HR, and how much is attributed to the two winding thermal ports HA and HB. The default value is 90%.

Ports

The block has the following ports:

A+

Top A-phase electrical connection.

A-

Lower A-phase electrical connection

B+

Top B-phase electrical connection.

B-

Lower B-phase electrical connection.

C

Mechanical rotational conserving port.

R

Mechanical rotational conserving port.

HA

Winding A thermal port. For more information, see Thermal Ports.

HB

Winding B thermal port. For more information, see Thermal Ports.

HR

Rotor thermal port. For more information, see Thermal Ports.

Examples

See the Controlled Stepper Motor example.

References

[1] M. Bodson, J. N. Chiasson, R. T. Novotnak and R. B. Rekowski. "High-Performance Nonlinear Feedback Control of a Permanent Magnet Stepper Motor." IEEE Transactions on Control Systems Technology, Vol. 1, No. 1, March 1993.

[2] P. P. Acarnley. Stepping Motors: A Guide to Modern Theory and Practice. New York: Peregrinus, 1982.

[3] S.E. Lyshevski. Electromechanical Systems, Electric Machines, and Applied Mechatronics. CRC, 1999.

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